# Properties

 Label 156.2.b Level $156$ Weight $2$ Character orbit 156.b Rep. character $\chi_{156}(25,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $56$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$156 = 2^{2} \cdot 3 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 156.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$56$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(156, [\chi])$$.

Total New Old
Modular forms 34 4 30
Cusp forms 22 4 18
Eisenstein series 12 0 12

## Trace form

 $$4 q + 4 q^{9} + O(q^{10})$$ $$4 q + 4 q^{9} + 4 q^{13} + 8 q^{17} - 16 q^{23} - 12 q^{25} - 8 q^{29} - 16 q^{35} + 8 q^{39} - 4 q^{49} - 16 q^{51} + 24 q^{53} + 24 q^{61} - 16 q^{65} - 16 q^{69} + 16 q^{75} + 48 q^{77} - 16 q^{79} + 4 q^{81} + 16 q^{87} + 16 q^{91} + 48 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(156, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
156.2.b.a $2$ $1.246$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}-\zeta_{6}q^{5}+q^{9}-\zeta_{6}q^{11}+(-1+\cdots)q^{13}+\cdots$$
156.2.b.b $2$ $1.246$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}+iq^{5}+2iq^{7}+q^{9}-3iq^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(156, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(156, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 2}$$